Some of the challenges of FL over wireless networks have been studied in [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
To minimize latency, a broadband analog aggregation multi-access scheme for FL was designed in [1]}.
The authors in [2]} proposed an FL implementation scheme between devices and access point over Gaussian multiple-access channels.
To improve the statistical learning performance for on-device distributed training, the authors in [3]} developed a sparse and low-rank modeling approach.
The work in in [4]} proposed
an energy-efficient strategy for bandwidth allocation
with the goal of reducing devices'
sum energy consumption while meeting the required learning performance.
However, the prior works [11]}, [1]}, [2]}, [3]}, [4]} focused on the delay/energy consumption for wireless consumption without considering the delay/energy tradeoff between learning and transmission.
Recently, in [5]} and [6]}, the authors considered both local learning and wireless transmission energy.
In [5]}, the authors investigated the FL loss function minimization problem with taking into account packet errors over wireless links.
However, this prior work ignored the computation delay of local FL model.
The authors in [6]} considered the sum learning and transmission energy minimization problem for FL,
where all users transmit learning results to the BS.
However, the solution in [6]} requires all users to upload their learning model synchronously.
